Abstract
A three-body semiclassical model is proposed to describe the nucleon transfer and emission reactions in a heavy-ion collision. In this model the two heavy particles, i.e. nuclear cores A$_1(Z_{A_1}, M_{A_1})$ and A$_2(Z_{A_2}, M_{A_2})$, move along classical trajectories $\vec R_1(t)$ and $\vec R_2(t)$ respectively, while the dynamics of the lighter neutron, n, is considered from a quantum mechanical point of view. Here, $M_i$ are the nucleon masses and $Z_i$ are the Coulomb charges of the heavy nuclei ($i=1,2$). A Faddeev-type semiclassical formulation using realistic paired nuclear-nuclear potentials is applied so that all three channels (elastic, rearrangement and break-up) are described in an unified manner. In order to solve these time-dependent equations the Faddeev components of the total three-body wave-function are expanded in terms of the input and output channel target eigenfunctions. In the special case when the nuclear cores are identical (A$_1 \equiv$ A$_2$) and the two-level approximation in the expansion over target functions the time-dependent semiclassical Faddeev equations are resolved in an explicit way. To determine the realistic $\vec R_1(t)$ and $\vec R_2(t)$ trajectories of the nuclear cores a self-consistent approach based on the Feynman path integral theory is applied.
Highlights
We have formulated a semiclassical approach for a model three-body system with two heavy nuclear cores A1 and A2 moving along classical trajectories and a lighter particle n, i.e. a neutron
The quantum dynamics of the neutron is described based on the few-body quantum-mechanical Eqs. (5)-(6) with realistic nuclear-nuclear potentials V13(x) and V23(y)
The classical dynamics of A1 and A2 are described based on Newtonian mechanics Eq (35)
Summary
Semiclassical methods and models, such as [19], allow us to gain even deeper insight into different few-body or many-body physical systems They enable us to introduce even more realistic classical trajectories of heavier particles in models, i.e. to take into account quantum-mechanical corrections in a self-consistent manner [19]. The heavy nuclei A1(ZA1 , MA1 ) and A2(ZA2 , MA2 ) move along realistic classical trajectories R1(t) and R2(t), while the motion of the relatively light neutron n (mn MAi ) in their nuclear fields is treated from a quantum-mechanical point of view In this model the heavy particles can move along complex Coulomb trajectories.
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